Existence of global solutions to a quasilinear wave equation with general nonlinear damping

Abstract

In this paper we prove the existence of a global solution and study its decay for the solutions to a quasilinear wave equation with a general nonlinear dissipative term by constructing a stable set in $H^{2}cap H_{0}^{1}$. Submitted July 02, 2002. Published October 26, 2002. Math Subject Classifications: 35B40, 35L70, 35B37. Key Words: Quasilinear wave equation; global existence; asymptotic behavior; nonlinear dissipative term; multiplier method.

Keywords

• Quasilinear wave equation
• global existence
• asymptotic behavior
• nonlinear dissipative term
• multiplier method.